A representative of Constellation was not immediately available for comment.

Shares of Constellation rose 4 percent, to $34.40, on Wednesday amid reports of a potential sale. Platts, an energy information company, first reported the possible deal. Exelon shares rose slightly on Wednesday, to $41.49, giving the company a market value of $27.5 billion.

Utilities have sought to combine to gain more customers, in part to fight falling prices. One of the largest deals announced this year is the $13.7 billion all-stock merger of Duke Energy and Progress Energy.

Constellation, based in Baltimore, has tried to sell itself before. Two years ago, it agreed to sell itself to Berkshire Hathaway’s MidAmerican Energy Holdings for $4.7 billion — only to cancel that deal in favor of selling nuclear assets to Électricité de France for $4.5 billion.

Exelon has also stumbled in previous deal-making attempts. It pursued a $7.5 billion hostile bid for NRG Energy beginning in 2008, only to drop its offer after failing to win over NRG’s shareholders.

Correction: April 27, 2011An earlier version of this article incorrectly stated the premium in the reported takeover offer as 18 percent.